So you are looking at being there the first half of July, that means mid-winter in the southern hemisphere. I would start with that.

Cape Town - not the best time to be there, as it can be cold and wet, equally you can have some beautiful days, it really is in the lap of the gods.
Kruger - winter is the dry season, and the later in the season you get the better the game viewing gets. July is a good time, still a bit away from the best time which would generally be at the end of the dry season. The day times in the safari areas will likely be glorious weather, but the early mornings and evenings will be very cool - they can get down to freezing in Kruger.
Victoria Falls - July is a good time to be there. The water is receding, but in July is usually still pretty spectacular - in July, I would personally suggest the Zimbabwe side. It is also a good time to visit Chobe, as it is starting to dry out and more game is starting to come down regularly to the river. Like in the Kruger area the days are likely to be fantastic, and the nights cool (though not as cold as Kruger).

I would maybe suggest something as follows:

3 July - DXB - CPT - day to relax and unwind. Remember your body clock is still going to be on LA time to a large degree. Hence I don't recommend starting with the safari as 6AM South Africa time wake up, will be around midnight/1AM for your body clock.
4 July - take a city tour, go up Table Mountain
5 July - full day Cape Peninsula tour - which will include a visit to the penguins.
6 July - you could split up this day - some doing shark cage diving and some doing winelands
7 July - fly Cape Town to Kruger - there are daily non-stop flight from Cape Town to 3 different airports in the Kruger region - MQP - Kruger Mpumalanga Airport just outside the park in the south, SZK - Skukuza Airport, inside the park in the southern area, and HDS - Eastgate/Hoedspruit Airport, just outside the park, but the access point to the private reserves like Timbavati, Thornybush, Kapama etc, as well as the central park. Which airport you fly into will probably be determined by which lodge you choose to visit. I would maybe recommend different options depending on how many of you end up travelling and what your room configuration would be. PM on safari at your lodge
8 July - on safari
9 July - on safari
10 July - AM on safari then flight to Johannesburg. Depending on flight time an afternoon city tour. Johannesburg has a much maligned reputation - and is actually quite a vibrant city, as long as you travel in safe hands.
11 July - Johannesburg to Victoria Falls. Afternoon visit the falls.
12 July - Full day for optional activities in the falls - there is a lot of choice here, depending on what you like, from white water rafting and bungee jumping to helicopters or paragliding over the falls etc. It is known as the adventure capital of Africa.
13 July - Victoria Falls - Johannesburg -> you would be in time for the early or late evening EK flight to DXB if that is the route you are taking. I gather the HK is Hong Kong - in which case you would also be able to connect to the SA flight JNB-HKG
Happy to help with rates if you need.